Assuming that gaseous reactants and products are present at...

Assuming that gaseous reactants and products are present at 1 atm partial pressure, which of the following reactions are spontaneous in the forward direction? (a) $\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(l) ; K_{\mathrm{p}}=7 \times 10^{-27}$ (b) $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) ; K_{\mathrm{p}}=2 \times 10^{198}$ (c) $\mathrm{MgCO}_{3}(s) \longrightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{CO}_{2}(g) ; K_{\mathrm{p}}=9 \times 10^{-10}$ (d) $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) ; K_{\mathrm{p}}=1 \times 10^{90}$

Assuming that gaseous reactants and products are present at 1 atm partial pressure, which of the following reactions are spontaneous in the forward direction?
(a) $\mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(l) ; K_{\mathrm{p}}=7 \times 10^{-27}$
(b) $2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) ; K_{\mathrm{p}}=2 \times 10^{198}$
(c) $\mathrm{MgCO}_{3}(s) \longrightarrow \mathrm{MgO}(\mathrm{s})+\mathrm{CO}_{2}(g) ; K_{\mathrm{p}}=9 \times 10^{-10}$
(d) $2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) ; K_{\mathrm{p}}=1 \times 10^{90}$

Key Concepts

Equilibrium Constant (K)

The equilibrium constant is a numerical value that quantifies the ratio of products to reactants at equilibrium under a given set of conditions. When expressed in terms of partial pressures (Kp), it indicates how much a reaction will favor the formation of products or remain with reactants when all gaseous components are at specified pressures.

Gibbs Free Energy (?G)

Gibbs free energy is a thermodynamic potential that indicates the spontaneity of a chemical reaction at constant temperature and pressure. The relationship ?G = -RT ln K shows that if the equilibrium constant (K) is greater than one, ?G is negative, rendering the forward reaction spontaneous under standard conditions.

Reaction Spontaneity

Reaction spontaneity is determined by the sign of the Gibbs free energy change. A negative ?G indicates that the forward reaction can proceed spontaneously, while a positive ?G suggests that the reverse reaction is favored in standard state conditions. This connection directly ties the equilibrium constant to the likelihood of a reaction proceeding in the forward direction.

Standard State Conditions

Standard state conditions refer to the set of typical conditions under which thermodynamic data is measured, commonly including reactants and products at 1 atm pressure for gases, 1 M concentrations for solutions, and pure substances for solids and liquids. Evaluating reactions under these conditions helps in using equilibrium constants and Gibbs free energies reliably to predict reaction direction.

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